Finite Group Databasebeta

← #25063621

Subgroups — #25063621

Order 11008.

1008 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148205C211yesmaximal, characteristic
2#19143725C211yesmaximal, characteristic, complemented
3#19143240C211yesmaximal, characteristic, complemented
4#19133059C212yesmaximal, complemented
5#19133045C211yesmaximal, characteristic, complemented
6#19133018C212yesmaximal, complemented
7#19133013C211yesmaximal, characteristic, complemented
8#19133002C212yesmaximal, complemented
9#19132984C212yesmaximal, complemented
10#19132977C211yesmaximal, characteristic, complemented
11C43×#1489C211yesmaximal, characteristic, complemented
12#14583634C411yescharacteristic
13#14583609C411yescharacteristic
14#14583606C411yescharacteristic
15#14583595—21no—
16#14583593C412yes—
17#14583573—22no—
18#14583545—21no—
19#14583537C412yes—
20D4×D172C411yescharacteristic
21#14583449C2211yescharacteristic
22#14583436C2212yes—
23#14583433—21no—
24#14583408—22no—
25C4×#10621898C2211yescharacteristic
26C2×C4×D172—21no—
27C4×D4×D43C2212yes—
28#14583023—21no—
29#14582976—21no—
30#14582975—22no—
31#14582961—22no—
32#14582952C2211yescharacteristic, complemented
33#14582951C2212yescomplemented
34#14582950C2212yescomplemented
35#14582950C2212yescomplemented
36#14582927—21no—
37#14582921C2212yescomplemented
38#14582867—21no—
39C2×C4×C43⋊C8C2211yescharacteristic, complemented
40Q8⋊(C43⋊C8)C2211yescharacteristic, complemented
41Q8⋊(C43⋊C8)C2211yescharacteristic, complemented
42#14582628C2212yescomplemented
43#14582628C2212yescomplemented
44D4⋊(C43⋊C8)C2211yescharacteristic
45D4⋊(C43⋊C8)C2211yescharacteristic
46#14582626C2212yescomplemented
47#14582626C2212yescomplemented
48C4×#41×C43C2211yescharacteristic
49C43×#423C2211yescharacteristic, complemented
50C4×M16×C43C2211yescharacteristic, complemented
51C43×Q8⋊C8C2212yescomplemented
52C43×D4⋊C8C2212yes—
53C2×#10621898—21no—
54C2×#10621898D411yescharacteristic
55C22×D172—21no—
56C2×D4×D43C2×C412yes—
57C22×C4×D43—22no—
58C2×#10621872—22no—
59C22×C43⋊C8—21no—
60#13063325C2×C411yescharacteristic
61#13063322C2×C411yescharacteristic
62#13063320—22no—
63#13063319—22no—
64#13063317—21no—
65#13063316C2×C412yes—
66#13063314C2×C412yes—
67#13063313—21no—
68#13063313—21no—
69#13063310—22no—
70#13063310—22no—
71#13063308—22no—
72#13063307—22no—
73#13063304—21no—
74#13063303—22no—
75#13063302—22no—
76#13063301C2×C412yes—
77#13063300C2×C412yes—
78#13063299—21no—
79#13063299—21no—
80#13063299C2×C412yes—
81#13063298—22no—
82#13063297—22no—
83#13063295—22no—
84#13063293—22no—
85C4×Dic86C2×C411yescharacteristic
86C4×Dic86D411yescharacteristic
87C4×D172—21no—
88C4×D172—22no—
89C4×D172—21no—
90C4×D172—22no—
91C4×D172—21no—
92C4×D172C2×C411yescharacteristic
93C4×D172D411yescharacteristic
94C4×D172C2312yes—
95D4×Dic43C2×C412yes—
96#13063287C2×C412yes—
97C4×C22⋊D43—22no—
98C4×C22⋊D43C2×C412yes—
99C4×C22⋊D43D412yes—
100(C22⋊D43)⋊C4—22no—
101#13063284D411yescharacteristic
102#13063282—22no—
103#13063282D412yes—
104C2×C4⋊Dic43—21no—
105C4⋊C4×D43C2×C412yes—
106C2×(C2×D43)⋊C4—22no—
107C22⋊C4×D43—22no—
108C42×D43C2312yes—
109C4⋊(C43⋊C8)C2311yescharacteristic
110C4⋊(C43⋊C8)C2311yescharacteristic
111Dic43⋊C8—22no—
112Dic43⋊C8—22no—
113Dic43⋊C8—22no—
114C22⋊(C43⋊C8)—21no—
115(C2×D43)⋊C8—22no—
116(C2×D43)⋊C8—22no—
117(C2×D43)⋊C8—22no—
118C4×C43⋊C8—21no—
119C4×C43⋊C8—21no—
120C4×C43⋊C8C2311yescharacteristic
121C4×C43⋊C8C2311yescharacteristic
122C8×Dic43—22no—
123C2×#41×C43C2×C411yescharacteristic
124C2×M16×C43—21no—
125C2×M16×C43—21no—
126C4×Q8×C43C2×C411yescharacteristic
127C4×Q8×C43C2311yescharacteristic
128C4×D4×C43—21no—
129C4×D4×C43—21no—
130C4×D4×C43C2×C411yescharacteristic
131C4×D4×C43C2311yescharacteristic
132#117×C43—21no—
133#117×C43C2×C411yescharacteristic
134C2×C42×C43—21no—
135C2×C42×C43C2311yescharacteristic
136C4⋊C8×C43—21no—
137C4⋊C8×C43C2312yes—
138#97×C43—21no—
139C4×C8×C43C2312yes—
140C23×D43—22no—
141#41×C43—22no—
142#41×C43—41no—
143C2×Q8×C43C22×C411yescharacteristic
144C2×D4×C43—21no—
145C2×D4×C43C22×C411yescharacteristic
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43C22×C411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C2×C22⋊D43—22no—
153C2×C22⋊D43—22no—
154C2×C22⋊D43C22⋊C412yes—
155C22×Dic43—22no—
156D4×D43—24no—
157D4×D43—42no—
158#10621898—42no—
159#10621898—81no—
160#10621898—81no—
161C2×D172—21no—
162C2×D172—21no—
163C2×D172—22no—
164C2×D172—44no—
165C2×D172C22⋊C411yescharacteristic
166C2×D172C22×C412yes—
167C2×C4×D43—22no—
168C2×C4×D43—22no—
169C2×C4×D43—22no—
170C2×C4×D43—82no—
171C2×C4×D43—82no—
172C2×C4×D43C22×C412yes—
173C2×C4×D43C2×D412yes—
174C2×C4×D43C2×D412yes—
175C2×Dic86—21no—
176C2×Dic86C22⋊C411yescharacteristic
177M16×C43—42no—
178M16×C43—81no—
179C2×C8×C43—22no—
180C2×C8×C43—22no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43C22×C411yescharacteristic
184C4⋊C4×C43C22×C411yescharacteristic
185C22⋊C4×C43—21no—
186C22⋊C4×C43—21no—
187C22⋊C4×C43—21no—
188C42×C43—21no—
189C42×C43—21no—
190C42×C43—21no—
191C42×C43C22×C411yescharacteristic
192C42×C43C2×D411yescharacteristic
193C42×C43C2×D411yescharacteristic
194C42×C43C2411yescharacteristic
195C22⋊Dic43—22no—
196C22⋊Dic43C22⋊C412yes—
197(C2×D43)⋊C4—22no—
198(C2×D43)⋊C4—22no—
199(C2×D43)⋊C4—22no—
200(C2×D43)⋊C4—22no—
201(C2×D43)⋊C4—22no—
202(C2×D43)⋊C4—22no—
203(C2×D43)⋊C4—22no—
204(C2×D43)⋊C4C22⋊C412yes—
205(C2×D43)⋊C4C22⋊C412yes—
206C4⋊Dic43—21no—
207C4⋊Dic43—22no—
208C4⋊Dic43C22⋊C411yescharacteristic
209C4⋊Dic43C22⋊C411yescharacteristic
210C4⋊Dic43C22×C412yes—
211Dic43⋊C4—22no—
212Dic43⋊C4—22no—
213Dic43⋊C4—22no—
214Dic43⋊C4C22⋊C412yes—
215Dic43⋊C4C22⋊C412yes—
216C4×Dic43C22×C412yes—
217C4×Dic43C2×D412yes—
218C4×Dic43C2×D412yes—
219C2×C43⋊C8—21no—
220C2×C43⋊C8—21no—
221C2×C43⋊C8—21no—
222C2×C43⋊C8—21no—
223C2×C43⋊C8—42no—
224#10621872—82no—
225C23×C43—21no—
226C23×C43C2×C22⋊C411yescharacteristic
227C22×D43—22no—
228C22×D43—44no—
229C22×D43—44no—
230C22×D43—82no—
231C22×D43C2×C22⋊C412yes—
232Q8×C43—21no—
233Q8×C43—21no—
234D4×C43—21no—
235D4×C43—42no—
236D4×C43#13112yes—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—22no—
242C2×C4×C43—21no—
243C2×C4×C43—21no—
244C2×C4×C43—21no—
245C2×C4×C43—42no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—42no—
249C2×C4×C43C2×C22⋊C411yescharacteristic
250C2×C4×C43C2×C22⋊C411yescharacteristic
251C2×C4×C43C2×C22⋊C411yescharacteristic
252C2×C4×C43C23×C411yescharacteristic
253C2×C4×C43C22×D411yescharacteristic
254C2×C4×C43C22×D411yescharacteristic
255C22⋊D43—42no—
256C22⋊D43—44no—
257C22⋊D43—82no—
258C2×Dic43—22no—
259C2×Dic43—82no—
260C2×Dic43C2×C22⋊C412yes—
261C2×Dic43C2×C22⋊C412yes—
262C2×Dic43C2×C22⋊C412yes—
263D172—22no—
264D172—22no—
265D172—22no—
266D172—44no—
267D172—42no—
268D172—81no—
269C4×D43—22no—
270C4×D43—22no—
271C4×D43—22no—
272C4×D43—22no—
273C4×D43—42no—
274C4×D43—42no—
275C4×D43—42no—
276C4×D43—82no—
277C4×D43—82no—
278Dic86—22no—
279Dic86—81no—
280C8×C43—42no—
281C8×C43—42no—
282C43⋊C8—41no—
283C43⋊C8—41no—
284C43⋊C8—41no—
285C43⋊C8—41no—
286#17522—431nomaximal, Sylow
287C22×C43—22no—
288C22×C43—21no—
289C22×C43—21no—
290C22×C43—21no—
291C22×C43—41no—
292C22×C43—41no—
293C22×C43C22×C22⋊C411yescharacteristic
294C2×D43—22no—
295C2×D43—22no—
296C2×D43—22no—
297C2×D43—42no—
298C2×D43—42no—
299C2×D43—42no—
300C2×D43—88no—
301C4×C43—21no—
302C4×C43—21no—
303C4×C43—21no—
304C4×C43—41no—
305C4×C43—41no—
306C4×C43—41no—
307C4×C43#42112yes—
308C4×C43C2×#13111yescharacteristic
309C4×C43#56811yescharacteristic
310C4×C43#57611yescharacteristic
311C4×C43#57711yescharacteristic
312Dic43—22no—
313Dic43—22no—
314Dic43—22no—
315Dic43—42no—
316#3481—431no—
317#2991—431no—
318#2922—431no—
319#1495—432no—
320#1492—431no—
321#1489D4311yescharacteristic, complemented
322#1486—432no—
323#1484—431no—
324#1482—432no—
325#1478—432no—
326#1476—431no—
327C2×C43—42no—
328C2×C43—41no—
329C2×C43#288011yescharacteristic
330C2×C43#289711yescharacteristic
331C2×C43C2×#42111yescharacteristic
332D43—42no—
333D43—82no—
334#559—431no—
335#554—431no—
336#554—431no—
337#553—432no—
338#553—861no—
339#551—862no—
340#546—432no—
341#546—861no—
342D42—431no—
343#532—431no—
344#529—432no—
345#529—861no—
346#525—862no—
347C4×#41—431no—
348C4×#41C2×D4311yescharacteristic
349C2×C4×D4—432no—
350C2×C4×D4—861no—
351C8×Q8—861no—
352#436—861no—
353#436—862no—
354#433—862no—
355#431—432no—
356#431—432no—
357#431—431no—
358#431—432no—
359#424—861no—
360#423—432no—
361#423C2×D4311yescharacteristic, complemented
362#408—861no—
363C4×M16C2×D4311yescharacteristic, complemented
364C2×C4×C8—431no—
365Q8⋊C8—431no—
366Q8⋊C8—431no—
367Q8⋊C8C2×D4312yescomplemented
368D4⋊C8—431no—
369D4⋊C8—431no—
370D4⋊C8—432no—
371D4⋊C8—432no—
372D4⋊C8—432no—
373D4⋊C8—432no—
374D4⋊C8C2×D4312yes—
375C43#1752211yescharacteristic, complemented, Sylow
376C2×#41—431no—
377C2×#41—861no—
378C2×#41C4×D4311yescharacteristic
379C22×D4—432no—
380C22×D4—861no—
381C23×C4—862no—
382C2×M16—21no—
383C2×M16—21no—
384C2×M16—862no—
385C22×C8—861no—
386C4⋊Q8—431no—
387#127—431no—
388#126—862no—
389#126—862no—
390#125—432no—
391#125—861no—
392#124—432no—
393#124—861no—
394#124—861no—
395#123—862no—
396#123—862no—
397#123—862no—
398#123—862no—
399C22⋊Q8—432no—
400C22⋊Q8—862no—
401C22⋊Q8—862no—
402C22⋊Q8—861no—
403#121—432no—
404#121—432no—
405#121—862no—
406#121—862no—
407#121—861no—
408#121—861no—
409#120—862no—
410#120—862no—
411C4×Q8—431no—
412C4×Q8—431no—
413C4×Q8C4×D4311yescharacteristic
414C4×Q8C22×D4311yescharacteristic
415C4×D4—21no—
416C4×D4—21no—
417C4×D4—432no—
418C4×D4—432no—
419C4×D4—432no—
420C4×D4—432no—
421C4×D4—431no—
422C4×D4—431no—
423C4×D4—432no—
424C4×D4—862no—
425C4×D4—861no—
426C4×D4—862no—
427C4×D4—861no—
428C4×D4—862no—
429C4×D4—862no—
430C4×D4—861no—
431C4×D4C4×D4311yescharacteristic
432C4×D4C22×D4311yescharacteristic
433#117—21no—
434#117—431no—
435#117—432no—
436#117—862no—
437#117C4×D4311yescharacteristic
438C2×C4⋊C4—432no—
439C2×C4⋊C4—861no—
440C2×C22⋊C4—862no—
441C2×C22⋊C4—862no—
442C2×C42—21no—
443C2×C42—432no—
444C2×C42C22×D4311yescharacteristic
445C4⋊C8—21no—
446C4⋊C8—431no—
447C4⋊C8—431no—
448C4⋊C8—862no—
449C4⋊C8—862no—
450C4⋊C8—862no—
451C4⋊C8C22×D4312yes—
452C22⋊C8—862no—
453C22⋊C8—862no—
454C22⋊C8—862no—
455C22⋊C8—861no—
456#97—21no—
457C4×C8—431no—
458C4×C8—431no—
459C4×C8—862no—
460C4×C8—861no—
461C4×C8—861no—
462C4×C8C22×D4312yes—
463C24—862no—
464#41—22no—
465#41—41no—
466#41—3441no—
467#41—3441no—
468#41—1722no—
469C2×Q8—431no—
470C2×Q8—861no—
471C2×Q8C2×C4×D4311yescharacteristic
472C2×D4—21no—
473C2×D4—432no—
474C2×D4—431no—
475C2×D4—432no—
476C2×D4—862no—
477C2×D4—862no—
478C2×D4—864no—
479C2×D4—862no—
480C2×D4—861no—
481C2×D4—861no—
482C2×D4—1724no—
483C2×D4—1722no—
484C2×D4C2×C4×D4311yescharacteristic
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—432no—
489C22×C4—432no—
490C22×C4—432no—
491C22×C4—862no—
492C22×C4—862no—
493C22×C4—862no—
494C22×C4—862no—
495C22×C4—3442no—
496C22×C4—3442no—
497C22×C4C2×C4×D4311yescharacteristic
498C22×C4D4×D4311yescharacteristic
499C22×C4D4×D4311yescharacteristic
500M16—42no—
501M16—81no—
502M16—3442no—
503C2×C8—22no—
504C2×C8—22no—
505C2×C8—861no—
506C2×C8—861no—
507C2×C8—861no—
508C2×C8—861no—
509C2×C8—1722no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—431no—
513C4⋊C4—431no—
514C4⋊C4—432no—
515C4⋊C4—432no—
516C4⋊C4—432no—
517C4⋊C4—862no—
518C4⋊C4—862no—
519C4⋊C4—862no—
520C4⋊C4—862no—
521C4⋊C4—861no—
522C4⋊C4C2×C4×D4311yescharacteristic
523C4⋊C4C2×C4×D4311yescharacteristic
524C22⋊C4—21no—
525C22⋊C4—21no—
526C22⋊C4—21no—
527C22⋊C4—432no—
528C22⋊C4—432no—
529C22⋊C4—432no—
530C22⋊C4—862no—
531C22⋊C4—862no—
532C22⋊C4—862no—
533C22⋊C4—862no—
534C22⋊C4—862no—
535C22⋊C4—862no—
536C22⋊C4—862no—
537C22⋊C4—862no—
538C42—21no—
539C42—21no—
540C42—21no—
541C42—432no—
542C42—432no—
543C42—432no—
544C42C2×C4×D4311yescharacteristic
545C42D4×D4311yescharacteristic
546C42D4×D4311yescharacteristic
547C42C23×D4311yescharacteristic
548C23—21no—
549C23—432no—
550C23—862no—
551C23—3442no—
552C23—1724no—
553C23—1724no—
554C23C22⋊C4×D4311yescharacteristic
555Q8—21no—
556Q8—21no—
557Q8—862no—
558Q8—3441no—
559D4—21no—
560D4—42no—
561D4—862no—
562D4—862no—
563D4—862no—
564D4—3441no—
565D4—3442no—
566D4—1724no—
567D4—1722no—
568D4—1724no—
569D4—1722no—
570D4#1306333312yes—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—22no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—432no—
584C2×C4—432no—
585C2×C4—432no—
586C2×C4—862no—
587C2×C4—862no—
588C2×C4—862no—
589C2×C4—862no—
590C2×C4—862no—
591C2×C4—3442no—
592C2×C4—3442no—
593C2×C4—3442no—
594C2×C4—1722no—
595C2×C4—1722no—
596C2×C4—1722no—
597C2×C4C22⋊C4×D4311yescharacteristic
598C2×C4C22⋊C4×D4311yescharacteristic
599C2×C4C22⋊C4×D4311yescharacteristic
600C2×C4C22×C4×D4311yescharacteristic
601C2×C4C2×D4×D4311yescharacteristic
602C2×C4C2×D4×D4311yescharacteristic
603C8—42no—
604C8—42no—
605C8—1721no—
606C8—1721no—
607C8—1721no—
608C8—1721no—
609C22—21no—
610C22—22no—
611C22—21no—
612C22—21no—
613C22—41no—
614C22—41no—
615C22—862no—
616C22—862no—
617C22—862no—
618C22—3448no—
619C22—1722no—
620C22—1722no—
621C22—1722no—
622C22C2×C22⋊C4×D4311yescharacteristic
623C4—21no—
624C4—21no—
625C4—21no—
626C4—41no—
627C4—41no—
628C4—41no—
629C4—862no—
630C4—862no—
631C4—862no—
632C4—1722no—
633C4#1458291412yes—
634C4C2×#1306333311yescharacteristic
635C4#1458366511yescharacteristic
636C4#1458370311yescharacteristic
637C4#1458370811yescharacteristic
638C2—41no—
639C2—42no—
640C2—3442no—
641C2—1722no—
642C2#1914304511yescharacteristic
643C2#1914311911yescharacteristic
644C2C2×#1458291411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1489C2
socleC22×C43C22×C22⋊C4
prime radical#19148205C2
cosocleC42×C43C24
hypercenter#1489D43
hypocenterC43#17522
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1489

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #19143725C2semidirect
3. #19143240C2semidirect
4. #19133059C2semidirect
5. #19133045C2semidirect
6. #19133018C2semidirect
7. #19133013C2semidirect
8. #19133002C2semidirect
9. #19132984C2semidirect
10. #19132977C2semidirect
11. C43×#1489C2semidirect
32. #14582952C22semidirect
33. #14582951C22semidirect
34. #14582950C22semidirect
35. #14582950C22semidirect
37. #14582921C22semidirect
39. C2×C4×C43⋊C8C22semidirect
40. Q8⋊(C43⋊C8)C22semidirect
41. Q8⋊(C43⋊C8)C22semidirect
42. #14582628C22semidirect
43. #14582628C22semidirect
46. #14582626C22semidirect
47. #14582626C22semidirect
49. C43×#423C22semidirect
50. C4×M16×C43C22semidirect
51. C43×Q8⋊C8C22semidirect
321. #1489D43semidirect
361. #423C2×D43semidirect
363. C4×M16C2×D43semidirect
367. Q8⋊C8C2×D43semidirect
375. C43#17522semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#191482052
#191437252
#191432402
#191330592
#191330452
#191330182
#191330132
#191330022
#191329842
#191329772
C43×#14892
#1752243